package com.wc.codeforces.二分.Robin_Hood_in_Town;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/**
 * @Author congge
 * @Date 2024/10/11 22:42
 * @description https://codeforces.com/problemset/problem/2014/C
 */
public class Main {
    static FastReader sc = new FastReader();
    static PrintWriter out = new PrintWriter(System.out);
    static int N = 200010;
    static long INF = (long) 2e12;
    static int[] a = new int[N];
    static int n, maxId = 0;
    static long sum = 0;

    public static void main(String[] args) {
        int T = sc.nextInt();
        while (T-- > 0) {
            n = sc.nextInt();
            sum = 0;
            maxId = 0;
            for (int i = 0; i < n; i++) {
                a[i] = sc.nextInt();
                if (a[maxId] < a[i]) maxId = i;
                sum += a[i];
            }
            long l = 0, r = INF;
            while (l < r) {
                long mid = l + r >> 1;
                if (check(mid)) r = mid;
                else l = mid + 1;
            }
            if (r == INF) r = -1;
            out.println(r);
        }
        out.flush();
    }

    static boolean check(long mid) {
        double avg = 1.0 * (mid + sum) / n;
        int num = 0;
        for (int i = 0; i < n; i++) {
            if (a[i] + (maxId == i ? mid : 0) < avg / 2) num++;
        }
        return num >= n / 2 + 1;
    }
}

class FastReader {
    StringTokenizer st;
    BufferedReader br;

    FastReader() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    String nextLine() {
        String s = "";
        try {
            s = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return s;
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    // 是否由下一个
    boolean hasNext() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                String line = br.readLine();
                if (line == null)
                    return false;
                st = new StringTokenizer(line);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return true;
    }
}
